I must admit, I'm enjoying Winds of Dune, which follows Dune Messiah in the timeline, except for flashbacks to Paul's youth and the middle years of the Jihad. I thought the flashbacks to Paul's youth were going to be crap, like in Paul of Dune, but they actually fit the bigger story very well so far. A lot more of the original characters in Winds of Dune, including Lady Jessica. The book was originally going to be called Jessica of Dune.
I also finally found an answer online as to why Paul started/allowed the Jihad. Once he passed a certain point in the original Dune story, teaching the oppressed Fremen how to defeat the Harkonnens and the Saurdukar, there was no stopping them. Paul had become their long-awaited Messiah. Even if he died, it would have continued in his name. He used it to fulfill his "terrible purpose", which was to reinvigorate the stagnant gene pool that had developed over thousands of years of relative peace in the Empire. The best way humans know how to do that is through fanatical bloody warfare. His son, Leto, the God Emperor of Dune, built on this, leading to the Golden Path, which scattered mankind across the universe and bred them so they couldn't be seen by enemies using prescience, assuring mankind's survival.